The South Wales Echo claim Sousa, who was linked with the vacant managerial position at Leicester City, has left the Swans.
The Portuguese coach was quickly installed as favourite to take over at the Foxes when Nigel Pearson quit to take charge at Hull City, but both clubs had denied any contact.
Huw Jenkins, the Swansea chairman, said as recently as Friday he had "not received an approach, in any shape or form, from Leicester City or any other club for his services".
Middlesbrough are believed to be closing in on the signing of forward Kris Boyd from Glasgow Rangers.